RunngDog,
The only difference is the body shape and size (and that the pickups come slanted on the LG, but you can get straight pickups is you like). The LG body is slightly smaller with a little more "carve" to the top, whereas the SKB is more traditional looking in that it's a little more symmetrical. Other than these minor variations, the basses are exactly the same and are priced similarly.

I've owned 2 LG models and 2 SKB models and I can't say that I've noticed any sound differences due to the body style. I will say that I prefer the way the SKB style looks (which is why both Roscoe's I currently own are SKB styles). I never had any neck dive problems with my LG models. I'm sure the wood choices could affect that though. I was pleasantly surprised that my SKB-3006 didn't suffer from neck dive. I was afraid that the extra neck wood might cause some problems in that area.
I'd go with the model that looks best to you! Also, for what it's worth, I'd highly recommend that you go with a Spanish Cedar core, Bart 3-band pre and Diamondwood fingerboard. Awesome sounding fretless bass!
Can I hear an amen Zon4John?